The figure above represents a piece of carpet in the shape of a trapezoid with the smaller base measuring 50 inches and the larger base measuring 70 inches. The other sides measure 12.5 inches and the height is 7.5 inches. What is the area of the carpet ?

My question:I do not understand, that when we have the heights, we cannot determine the length of the sides, because we can make a right triangle and we know two sides: 7,5 heights and 10 for the other side, when drawing the heights from one cornerpoint of the smaller side to the larger side. Then use =phytagoras and we know the missing side = 20

Okay, I think you are reading too much into this problem. The standard formula for finding the area of a trapezoid is (1/2)(B + b)h where B is the bigger base, b is the smaller base, and h is the height. So to find the area of the carpet we simply calculate the following:

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